Proving the Complex Conjugate of a Matrix Determinant

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The discussion focuses on proving the relationship det(A) = (det(A))* = det(A$), where * denotes the complex conjugate and $ denotes the transpose. Participants express confusion over the validity of the first half of the equality, noting it only holds if det(A) is real. The proof for det(A$) = det(A) is mentioned, emphasizing the use of determinant definitions and permutation properties. Clarification is sought regarding the meaning of det(A) = (det(A))* in the context of the problem. The conversation highlights the need for a deeper understanding of determinants in relation to complex matrices.
Kolahal Bhattacharya
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Homework Statement



show that det(A)=(detA)*= det(A$)
where * denotes complex conjugate and $ means transpose

Homework Equations





The Attempt at a Solution



Please help me to start the problem.I am not getting a way.
 
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You are posting problems faster than you are solving them. The first half of your equality is simply not true unless det(A) is real. Please reconsider.
 
The proof of det(A^T) = det(A) (at least the one I know about) is about using the definition of the determinant and the properties of permutations.

Further on, I'm not sure what you mean with det(A)=(detA)*.
 
Thread 'Correct statement about size of wire to produce larger extension'

Thread 'Correct statement about size of wire to produce larger extension'

The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
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